I think every state in the USA requires trailer brakes if the trailer is over 3000 pounds. A brake control is used when you have a trailer with electric brakes. When you push the brake peddle in the tow vehicle, the brake control sends an electric signal to the trailer brakes to activate them. Yes, you need this type of braking system when towing a travel trailer.
The other kind of braking system is a surge brake system. There is no separate attachments to the tow vehicle. All the braking mechanisms are in the trailer. Attached to the hitch coupler on the trailer is a surge sensor. What happens, when the tow vehicle slows down, the trailer continues to maintain it's speed. The tow vehicle is slowing, so the trailer is now pushing the tow vehicle. When this happens, the surge brake controller engages which activates the trailer brakes causing it to begin braking. The harder the tow vehicle brakes, the harder the surge, the greater the trailer brakes are activated. These systems are simply not a good match for a travel trailer. I've driven some like this and I found it to be a very jerky experience.
Sway bar. More than likely you'll want some kind of sway control system. There are basically 2 types. There are separate sway bars that attach separate to your hitching system and have a turn handle that actually tightens a brake pad in the bar. By tightning, this causes resistance which helps prevent the back end of the trailer from pulsating back and forth, (which is what sway is).
The second type is built into the weight distribution system. Weight Distribution distributes the trailer weight from the rear of the tow vehicle (squat in the rear) and moves that weight forward to the front axles, evenly dividing the weight on the tongue and hitch between the trailer and both axles of the tow vehicle. Yes, you will probably need this. Several kinds of weight distribution systems come with a built in sway feature. They all do the same thing, .... create resistance so it eliminates the rear of trailer from wiggling side to side.